Warren Buffett has built a sprawling $560 billion conglomerate with footholds in insurance, energy and railroads. Berkshire Hathaway Inc.’s reach is so wide, in fact, that its businesses sometimes bump into each other.

Buffett, in his annual letter to shareholders, recounted a story about a September fire at a French plant owned by Lubrizol, a maker of oil additives. The fire damaged the property and disrupted business, causing losses that would be lessened by insurance coverage. But, Buffett said, there’s a catch.

“One of the largest insurers of Lubrizol was a company owned by ... uh, Berkshire,” the billionaire investor said in the letter, released Saturday. “In Matthew 6:3, the Bible instructs us to ‘Let not the left hand know what the right hand doeth.’ Your chairman has clearly behaved as ordered.”